## Example Questions

### Example Question #1 : How To Factor A Common Factor Out Of Squares

Which real number satisfies ?      Explanation:

Simplify the base of 9 and 27 in order to have a common base.

(3x)(9)=272

= (3x)(32)=(33)2

=(3x+2)=36

Therefore:

x+2=6

x=4

### Example Question #1 : How To Factor A Common Factor Out Of Squares

Which of the following is a factor of ?      Explanation:

The terms of have as their greatest common factor, so  is a prime polynomial.

Of the five choices, only is a factor.

### Example Question #2 : How To Factor A Common Factor Out Of Squares

Simplify       Explanation:

The easiest way to approach this problem is to break everything into exponents. is equal to and 27 is equal to . Therefore, the expression can be broken down into . When you cancel out all the terms, you get , which equals .

### Example Question #30 : Powers & Roots Of Numbers

Which of the following expression is equal to       Explanation: When simplifying a square root, consider the factors of each of its component parts: Combine like terms: Remove the common factor, : Pull the outside of the equation as : ### Example Question #3 : Squaring / Square Roots / Radicals

Which of the following is equal to the following expression?       Explanation: First, break down the components of the square root: Combine like terms. Remember, when multiplying exponents, add them together: Factor out the common factor of :  Factor the : Combine the factored with the : Now, you can pull out from underneath the square root sign as : ### Example Question #1 : Squaring / Square Roots / Radicals

Which of the following expressions is equal to the following expression?       Explanation: First, break down the component parts of the square root: Combine like terms in a way that will let you pull some of them out from underneath the square root symbol: Pull out the terms with even exponents and simplify: ### Example Question #3 : How To Factor A Common Factor Out Of Squares

What is, ?      Explanation:

To find an equivalency we must rationalize the denominator.

To rationalize the denominator multiply the numerator and denominator by the denominator.  Factor out 6, Extract perfect square 9 from the square root of 18.   ### All ACT Math Resources 